If \(|\vec{a}| = 6\), \(|\vec{b}| = 5\) and \(\vec{a}\) is perpendicular to \(\vec{b}\), then \(|2\vec{a}-\vec{b}|\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 13
Since \(\vec{a}\) and \(\vec{b}\) are perpendicular, \(\vec{a}\cdot\vec{b} = 0\). Using \(|\vec{v}|^2 = \vec{v}\cdot\vec{v}\):
\(|2\vec{a}-\vec{b}|^2 = 4|\vec{a}|^2-4\,\vec{a}\cdot\vec{b}+|\vec{b}|^2\)
\( = 4(36)-0+25\)
\( = 169\)
\(|2\vec{a}-\vec{b}| = 13\)